PHYS08200604017 Manimala Mitra - Homi Bhabha National Institute

Majorana mass term breaks lepton number by two units. In the standard model with
only left-handed neutrino fields and lepton number conservation, Dirac or Majorana any
kind of neutrino mass is not possible to generate. Hence to explain the non-zero neutrino
mass, we must look for beyond standard model physics. In addition to the experimental
evidences of non-zero neutrino mass, the experiments also indicatate very tiny masses
of the standard model neutrino, which is at most O( eV). This extremely tiny mass
points towards a O(10 12 ) order of magnitude mass hierarchy between the top quark and
neutrino. The very elegant mechanism to explain the tiny Majorana neutrino mass is the
novel seesaw mechanism. Below we describe the mass generation mechanism of a Dirac
as well as of a Majorana neutrino.
2.2.1 Dirac Mass
The standard model can be extended by adding gauge singlet right handed neutrino N R .
The neutrino masses can be generated from the gauge invariant Yukawa Lagrangian. The
Yukawa Lagrangian which incorporates the right handed neutrino state is,
−L yuk = Y ν ¯NR ˜H† L+h.c (2.11)
Thestandardmodel HiggsH takes vacuumexpectation valuev andgeneratethefollowing
Dirac neutrino mass matrix,
m ν = Y ν v. (2.12)
For v ∼ 174 GeV, eV neutrino mass m ν constraints the Yukawa Y ν ∼ 10 −12 , which is
extremely tiny and leads to fine tuning problem into the theory.
2.2.2 Majorana Mass and Seesaw
The standard model neutrinos can be Majorana particles. The Majorana mass term of
the standard model neutrinos has been given in Eq. (2.10), which violates lepton number
by two units. The most elegant mechanism to explain the Majorana neutrino masses is
the seesaw mechanism [21]. The Lepton number violating Majorana mass term can be
from the dimension-5 Weinberg operator [22] Ô = κ ij
2 (LC i
˜H ∗ )( ˜H † L j ), where i,j denote
the generation indices and κ is the coupling-coefficient. After the electroweak symmetry
breaking and Higgs takes a vacuum expectation value v, this dimension-5 operator
generates the following Majorana mass term of the standard model neutrinos,
κ ij
2 (LC i
˜H ∗ )( ˜H † L j ) −→ κ ij
2 v2 ν C L i
ν Lj (2.13)
Considering the standard model as an effective low energy theory, the dimension-5 operator
Ô = LLHH [22,23] can be generated by integrating out some heavy modes of the full
M
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